Poker Odds, Permutations, Formulas, and Computations

As Dealt - 5 Card Draw/Stud, 7 Card Draw

12 Mar 06

Introduction

Very rudimentary at this time. Don't know what I'm going to put on this page, but not high on my "To Do" list.

Formulas

Basic 5-card poker hand - no joker -- Formula - ((52!/47!)/(5!)) -- Possibilities - 2,598,960
Basic 5-card poker hand - 1 joker -- Formula - ((53!/48!)/(5!)) -- Possibilities - 2,869,685
Basic 5-card poker hand - 2 jokers -- Formula - ((54!/49!)/(5!)) -- Possibilities - 3,162,510
Basic 7-card poker hand -- Formula - ((52!/45!)/(7!)) -- Possibilities - 133,784,560

Possibilities and Odds - As Dealt

5-Card - No Joker, No Wild Cards.

Royal Flush -- Possibilities - 4 -- Odds - 1::649,740.00
Straight Flush -- Possibilities - 36 -- Odds - 1::72,193.33
Full House -- Possibilities - 624 -- Odds - 1::4,165.00
Four of a Kind -- Possibilities - 3,744 -- Odds - 1::694.17
Flush -- Possibilities - 5,108 -- Odds - 1::508.80
Straight -- Possibilities - 10,200 -- Odds - 1::254.80
Three of a Kind -- Possibilities - 54,912 -- Odds - 1::47.33
Two Pair -- Possibilities - 123,552 -- Odds - 1::21.04
One Pair -- Possibilities - 1,098,240 -- Odds - 1::2.37
Bust Hand -- Possibilities - 1,302,540 -- Odds - 1::2.00

5-Card - 1 Joker, No Other Wild Cards.

Royal Flush -- Possibilities - Future -- Odds - Future
Straight Flush -- Possibilities - Future -- Odds - Future
Full House -- Possibilities - Future -- Odds - Future
Four of a Kind -- Possibilities - Future -- Odds - Future
Flush -- Possibilities - Future -- Odds - Future
Straight -- Possibilities - Future -- Odds - Future
Three of a Kind -- Possibilities - Future -- Odds - Future
Two Pair -- Possibilities - Future -- Odds - Future
One Pair -- Possibilities - Future -- Odds - Future
Bust Hand -- Possibilities - Future -- Odds - Future

5-Card - 2 Jokers, No Other Wild Cards.

Royal Flush -- Possibilities - Future -- Odds - Future
Straight Flush -- Possibilities - Future -- Odds - Future
Full House -- Possibilities - Future -- Odds - Future
Four of a Kind -- Possibilities - Future -- Odds - Future
Flush -- Possibilities - Future -- Odds - Future
Straight -- Possibilities - Future -- Odds - Future
Three of a Kind -- Possibilities - Future -- Odds - Future
Two Pair -- Possibilities - Future -- Odds - Future
One Pair -- Possibilities - Future -- Odds - Future
Bust Hand -- Possibilities - Future -- Odds - Future

7-Card - No Joker, No Wild Cards.

Royal Flush -- Possibilities - Future -- Odds - Future
Straight Flush -- Possibilities - Future -- Odds - Future
Full House -- Possibilities - Future -- Odds - Future
Four of a Kind -- Possibilities - Future -- Odds - Future
Flush -- Possibilities - Future -- Odds - Future
Straight -- Possibilities - Future -- Odds - Future
Three of a Kind -- Possibilities - Future -- Odds - Future
Two Pair -- Possibilities - Future -- Odds - Future
One Pair -- Possibilities - Future -- Odds - Future
Bust Hand -- Possibilities - Future -- Odds - Future

Chart Progress

5 Card Hands - No Joker
Hands	Quantity	Percentage
Possible	2598960	100.000000
Processed	2598960	100.000000
Posted	2598960	100.000000

7 Card Hands
Hands	Quantity	Percentage
Possible	133784560	100.000000
Processed	0	0.000000
Posted	0	0.000000

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